The generator matrix

 1  0  0  1  1  1  X  1  1  2  1  1  1  1
 0  1  0  1 X+2 X+3  1  0  3  1  0 X+2 X+1 X+1
 0  0  1  1 X+3 X+2  1 X+2 X+1  X  0 X+1  0  0
 0  0  0  2  0  0  0  0  0  2  0  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  2  0  0
 0  0  0  0  0  2  0  0  2  2  0  2  2  2
 0  0  0  0  0  0  2  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  0  2  2  0  0

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+59x^8+80x^9+376x^10+848x^11+2152x^12+2144x^13+5040x^14+2144x^15+2207x^16+848x^17+344x^18+80x^19+56x^20+5x^24

The gray image is a code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.423 seconds.